Matlab 全局搜索功能：错误消息，无法开始搜索最小值

Question

我有一个矩阵方程组，我想在其中找到 2 个 7x7 矩阵（所以我正在使用 (1x98) 向量）。

我想使用 GlobalSearch Matlab 函数时遇到问题。这是我的代码：

Eq1 = (P1.')*(a.')*a*P1 + (P1.')*(a.')*b*P2 + (P2.')*(b.')*a*P1 + (P2.')*(b.')*b*P2 - eye(7);
Eq2 = F1*a*P1 + F1*b*P2 + F2*a*P1 + F2*b*P2 - (a*P1 + b*P2)*D;
Eqs = reshape([Eq1,Eq2],2*7*7,[]);
Fun = matlabFunction(Eqs);

F = @(x) Fun(...
    x(  1   ),  x(  2   ),  x(  3   ),  x(  4   ),  x(  5   ),  x(  6   ),  x(  7   ),...
    x(  8   ),  x(  9   ),  x(  10  ),  x(  11  ),  x(  12  ),  x(  13  ),  x(  14  ),...
    x(  15  ),  x(  16  ),  x(  17  ),  x(  18  ),  x(  19  ),  x(  20  ),  x(  21  ),...
    x(  22  ),  x(  23  ),  x(  24  ),  x(  25  ),  x(  26  ),  x(  27  ),  x(  28  ),...
    x(  29  ),  x(  30  ),  x(  31  ),  x(  32  ),  x(  33  ),  x(  34  ),  x(  35  ),...
    x(  36  ),  x(  37  ),  x(  38  ),  x(  39  ),  x(  40  ),  x(  41  ),  x(  42  ),...
    x(  43  ),  x(  44  ),  x(  45  ),  x(  46  ),  x(  47  ),  x(  48  ),  x(  49  ),...
    x(  50  ),  x(  51  ),  x(  52  ),  x(  53  ),  x(  54  ),  x(  55  ),  x(  56  ),...
    x(  57  ),  x(  58  ),  x(  59  ),  x(  60  ),  x(  61  ),  x(  62  ),  x(  63  ),...
    x(  64  ),  x(  65  ),  x(  66  ),  x(  67  ),  x(  68  ),  x(  69  ),  x(  70  ),...
    x(  71  ),  x(  72  ),  x(  73  ),  x(  74  ),  x(  75  ),  x(  76  ),  x(  77  ),...
    x(  78  ),  x(  79  ),  x(  80  ),  x(  81  ),  x(  82  ),  x(  83  ),  x(  84  ),...
    x(  85  ),  x(  86  ),  x(  87  ),  x(  88  ),  x(  89  ),  x(  90  ),  x(  91  ),...
    x(  92  ),  x(  93  ),  x(  94  ),  x(  95  ),  x(  96  ),  x(  97  ),  x(  98  ));

x0 =  ones(2*7*7,1);
gs = GlobalSearch;
options = optimoptions('fmincon','Algorithm', 'interior-point',...
    'UseParallel',true, 'Display','off','MaxFunctionEvaluations',6000, 'TolCon', 1e-4, 'TolFun', 1e-4);
problem = createOptimProblem('fmincon', ...
'objective',F, ...
'x0',x0, ...
'lb',[-1*ones(98)], ...
'ub',[1*ones(98)], ...
'options',options)
[x,fval] = run(gs,problem)

但不幸的是，我在执行时遇到以下错误：

problem =

  struct with fields:

    objective: [function_handle]
           x0: [98x1 double]
        Aineq: []
        bineq: []
          Aeq: []
          beq: []
           lb: [98x98 double]
           ub: [98x98 double]
      nonlcon: []
       solver: 'fmincon'
      options: [1x1 optim.options.Fmincon]

Warning: Length of lower bounds is > length(x); ignoring extra bounds.
> In checkbounds (line 27)
  In checkglobalsearchnlpinputs (line 36)
  In globalsearchnlp
  In GlobalSearch/run (line 340)
  In compute_solving_Matricial_Global (line 96)
Warning: Length of upper bounds is > length(x); ignoring extra bounds.
> In checkbounds (line 41)
  In checkglobalsearchnlpinputs (line 36)
  In globalsearchnlp
  In GlobalSearch/run (line 340)
  In compute_solving_Matricial_Global (line 96)
Error using fmincon (line 635)
Supplied objective function must return a scalar value.

Error in globalsearchnlp

Error in GlobalSearch/run (line 340)
                globalsearchnlp(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,options,localOptions);

Error in compute_solving_Matricial_Global (line 96)
[x,fval] = run(gs,problem)

Caused by:
    Failure in initial call to fmincon with user-supplied problem structure.

如何修复此错误消息？

我认为我正确地使用了 GlobalSearch，但这个问题可能来自不正确的下限或上限，甚至是我使用的向量大小。

Answer 1

不，这不是尺寸问题。虽然由于代码不完整我们无法重现错误，但错误信息很明确：

Supplied objective function must return a scalar value.

Tyr 使用静态向量调用 F 并检查其结果的大小。它应该 return 一个单一的值。

但是也有关于upper/lower边界的警告：

...
      x0: [98x1 double]
...
      lb: [98x98 double]
      ub: [98x98 double]
...

根据 fmincon 文档：

x0 — Initial point

Initial point, specified as a real vector or real array. Solvers use the number of elements in, and size of, x0 to determine the number and size of variables that fun accepts.

现在，您指定 x0 为 2*7*7 by 1，而 lb 和 ub 为 98 by 98。它们应该都一样大。

Matlab 全局搜索功能：错误消息，无法开始搜索最小值

Matlab's GlobalSearch function : error message and can't start the searching for minimum

matlab

solver

equation-solving

fminsearch